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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <unsupported/Eigen/Polynomials>
#include <iostream>
#include <algorithm>
using namespace std;
namespace Eigen {
namespace internal {
template<int Size>
struct increment_if_fixed_size
{
enum {
ret = (Size == Dynamic) ? Dynamic : Size+1
};
};
}
}
template<int Deg, typename POLYNOMIAL, typename SOLVER>
bool aux_evalSolver( const POLYNOMIAL& pols, SOLVER& psolve )
{
typedef typename POLYNOMIAL::Index Index;
typedef typename POLYNOMIAL::Scalar Scalar;
typedef typename SOLVER::RootsType RootsType;
typedef Matrix<Scalar,Deg,1> EvalRootsType;
const Index deg = pols.size()-1;
psolve.compute( pols );
const RootsType& roots( psolve.roots() );
EvalRootsType evr( deg );
for( int i=0; i<roots.size(); ++i ){
evr[i] = std::abs( poly_eval( pols, roots[i] ) ); }
bool evalToZero = evr.isZero( test_precision<Scalar>() );
if( !evalToZero )
{
cerr << "WRONG root: " << endl;
cerr << "Polynomial: " << pols.transpose() << endl;
cerr << "Roots found: " << roots.transpose() << endl;
cerr << "Abs value of the polynomial at the roots: " << evr.transpose() << endl;
cerr << endl;
}
std::vector<Scalar> rootModuli( roots.size() );
Map< EvalRootsType > aux( &rootModuli[0], roots.size() );
aux = roots.array().abs();
std::sort( rootModuli.begin(), rootModuli.end() );
bool distinctModuli=true;
for( size_t i=1; i<rootModuli.size() && distinctModuli; ++i )
{
if( internal::isApprox( rootModuli[i], rootModuli[i-1] ) ){
distinctModuli = false; }
}
VERIFY( evalToZero || !distinctModuli );
return distinctModuli;
}
template<int Deg, typename POLYNOMIAL>
void evalSolver( const POLYNOMIAL& pols )
{
typedef typename POLYNOMIAL::Scalar Scalar;
typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
PolynomialSolverType psolve;
aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve );
}
template< int Deg, typename POLYNOMIAL, typename ROOTS, typename REAL_ROOTS >
void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const REAL_ROOTS& real_roots )
{
typedef typename POLYNOMIAL::Scalar Scalar;
typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
PolynomialSolverType psolve;
if( aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ) )
{
//It is supposed that
// 1) the roots found are correct
// 2) the roots have distinct moduli
typedef typename POLYNOMIAL::Scalar Scalar;
typedef typename REAL_ROOTS::Scalar Real;
typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
typedef typename PolynomialSolverType::RootsType RootsType;
typedef Matrix<Scalar,Deg,1> EvalRootsType;
//Test realRoots
std::vector< Real > calc_realRoots;
psolve.realRoots( calc_realRoots );
VERIFY( calc_realRoots.size() == (size_t)real_roots.size() );
const Scalar psPrec = internal::sqrt( test_precision<Scalar>() );
for( size_t i=0; i<calc_realRoots.size(); ++i )
{
bool found = false;
for( size_t j=0; j<calc_realRoots.size()&& !found; ++j )
{
if( internal::isApprox( calc_realRoots[i], real_roots[j] ), psPrec ){
found = true; }
}
VERIFY( found );
}
//Test greatestRoot
VERIFY( internal::isApprox( roots.array().abs().maxCoeff(),
internal::abs( psolve.greatestRoot() ), psPrec ) );
//Test smallestRoot
VERIFY( internal::isApprox( roots.array().abs().minCoeff(),
internal::abs( psolve.smallestRoot() ), psPrec ) );
bool hasRealRoot;
//Test absGreatestRealRoot
Real r = psolve.absGreatestRealRoot( hasRealRoot );
VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
if( hasRealRoot ){
VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), internal::abs(r), psPrec ) ); }
//Test absSmallestRealRoot
r = psolve.absSmallestRealRoot( hasRealRoot );
VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
if( hasRealRoot ){
VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), internal::abs( r ), psPrec ) ); }
//Test greatestRealRoot
r = psolve.greatestRealRoot( hasRealRoot );
VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
if( hasRealRoot ){
VERIFY( internal::isApprox( real_roots.array().maxCoeff(), r, psPrec ) ); }
//Test smallestRealRoot
r = psolve.smallestRealRoot( hasRealRoot );
VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
if( hasRealRoot ){
VERIFY( internal::isApprox( real_roots.array().minCoeff(), r, psPrec ) ); }
}
}
template<typename _Scalar, int _Deg>
void polynomialsolver(int deg)
{
typedef internal::increment_if_fixed_size<_Deg> Dim;
typedef Matrix<_Scalar,Dim::ret,1> PolynomialType;
typedef Matrix<_Scalar,_Deg,1> EvalRootsType;
cout << "Standard cases" << endl;
PolynomialType pols = PolynomialType::Random(deg+1);
evalSolver<_Deg,PolynomialType>( pols );
cout << "Hard cases" << endl;
_Scalar multipleRoot = internal::random<_Scalar>();
EvalRootsType allRoots = EvalRootsType::Constant(deg,multipleRoot);
roots_to_monicPolynomial( allRoots, pols );
evalSolver<_Deg,PolynomialType>( pols );
cout << "Test sugar" << endl;
EvalRootsType realRoots = EvalRootsType::Random(deg);
roots_to_monicPolynomial( realRoots, pols );
evalSolverSugarFunction<_Deg>(
pols,
realRoots.template cast <
std::complex<
typename NumTraits<_Scalar>::Real
>
>(),
realRoots );
}
void test_polynomialsolver()
{
for(int i = 0; i < g_repeat; i++)
{
CALL_SUBTEST_1( (polynomialsolver<float,1>(1)) );
CALL_SUBTEST_2( (polynomialsolver<double,2>(2)) );
CALL_SUBTEST_3( (polynomialsolver<double,3>(3)) );
CALL_SUBTEST_4( (polynomialsolver<float,4>(4)) );
CALL_SUBTEST_5( (polynomialsolver<double,5>(5)) );
CALL_SUBTEST_6( (polynomialsolver<float,6>(6)) );
CALL_SUBTEST_7( (polynomialsolver<float,7>(7)) );
CALL_SUBTEST_8( (polynomialsolver<double,8>(8)) );
CALL_SUBTEST_9( (polynomialsolver<float,Dynamic>(
internal::random<int>(9,13)
)) );
CALL_SUBTEST_10((polynomialsolver<double,Dynamic>(
internal::random<int>(9,13)
)) );
}
}
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